大尺度发电机跃迁的研究
Study on the large scale dynamo transition
摘要：
利用磁流体动力学（MHD）描述，建立了一个非线性发电机模型，该模型通过电动势（e.m.f.）在大规模的感应方程中。本文用MHD速度场和磁场涨落的壳模型描述了等离子体在小尺度下的非线性行为，壳模型允许在大参数范围内研究这一问题，这是许多自然系统中发电机现象的特征，也是目前超级计算机所不能解决的问题。在等离子体湍流状态的特定条件下，小尺度的场涨落能够触发发电机不稳定性。我们研究这种过渡考虑的稳定性曲线，这表明了强烈的减少临界磁雷诺数增加逆磁Prandlt数$\textrm{Pm}^{-1}$的范围$[10^{-6},1]$和减缓范围$[1,10^{8}]$的增加。我们也得到滞后行为的发电机边界揭示了这种过渡的亚临界性质。该系统，经历这种转变，可以达到不同的发电机制度，这取决于雷诺数的等离子体流。这显示了湍流在发电机现象中所起的关键作用。特别是该模型是能够再现的动态情况下，大规模的磁场之间的跳跃两个状态，代表相反的极性的磁场，再现地磁发电机和VKS实验中观察到的磁反转。
英文摘要：
Using the magnetohydrodynamic (MHD) description, we develop a nonlinear dynamo model that couples the evolution of the large scale magnetic field with turbulent dynamics of the plasma at small scale by electromotive force (e.m.f.) in the induction equation at large scale. The nonlinear behavior of the plasma at small scale is described by using a MHD shell model for velocity field and magnetic field fluctuations.The shell model allow to study this problem in a large parameter regime which characterizes the dynamo phenomenon in many natural systems and which is beyond the power of supercomputers at today. Under specific conditions of the plasma turbulent state, the field fluctuations at small scales are able to trigger the dynamo instability. We study this transition considering the stability curve which shows a strong decrease in the critical magnetic Reynolds number for increasing inverse magnetic Prandlt number $\textrm{Pm}^{-1}$ in the range $[10^{-6},1]$ and slows an increase in the range $[1,10^{8}]$. We also obtain hysteretic behavior across the dynamo boundary reveling the subcritical nature of this transition. The system, undergoing this transition, can reach different dynamo regimes, depending on Reynolds numbers of the plasma flow. This shows the critical role that the turbulence plays in the dynamo phenomenon. In particular the model is able to reproduce the dynamical situation in which the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field, reproducing the magnetic reversals as observed in geomagnetic dynamo and in the VKS experiments.
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